How to use the Circle Calculator
- Measure the radius — the distance from the centre to the edge.
- If you only have the diameter, halve it before entering.
- Enter the radius in whatever unit you are working in.
- Read the circumference for anything involving edging, belts or perimeter.
- Read the area for material coverage, flow cross-sections or paint quantities.
How the calculation works
Every circle shares the same ratio between circumference and diameter, and that constant is pi. From it, both key results follow: the circumference is pi times the diameter, or equivalently two pi times the radius, and the area is pi times the radius squared. The area formula can be pictured by cutting the disc into thin wedges and rearranging them into a near-rectangle of height r and length half the circumference — the product is pi r².
The squared term in the area formula is what surprises people. Doubling the radius doubles the circumference but quadruples the area. A 16-inch pizza carries not 33% but 78% more food than a 12-inch one, and a pipe of twice the bore carries roughly four times the flow at the same velocity. Whenever a decision compares circular things by their linear size, the area relationship is the one that actually matters.
Precision matters less than people fear. Using 3.14 instead of full pi introduces an error of about 0.05%, which is invisible next to any real measurement tolerance. What does matter is measuring the radius accurately, since its error is squared in the area: a 2% error in radius becomes a 4% error in area. Measure the diameter across the widest span and halve it — that is more reliable than trying to locate the centre by eye.
d = 2r; C = 2πr; A = πr²Source: Classical results attributed to Archimedes, Measurement of a Circle (c. 250 BCE); pi per NIST fundamental constants.
Worked example
A circular patio of 3.6 m diameter needs edging and paving.
- Radius: 3.6 / 2 = 1.8 m.
- Circumference: 2 × π × 1.8 = 11.31 m of edging.
- Area: π × 1.8² = π × 3.24 = 10.18 m².
- Add 10% waste to the paving: 10.18 × 1.1 = 11.2 m².
11.31 m of edging and about 11.2 m² of paving once cutting waste is allowed for.
Frequently asked questions
How do I work backwards from area to radius?+
Divide the area by pi and take the square root. A 50 m² circle has a radius of √(50/π) = 3.99 m.
Does this cover ellipses?+
No. An ellipse's area is pi times the two semi-axes multiplied together, and its perimeter has no simple closed form at all.
Why is the answer never exact?+
Pi is irrational, so any decimal is a truncation. The calculator carries about 16 significant digits, far beyond any physical measurement.
What about the area of a ring?+
Subtract the inner circle from the outer: π(R² − r²). That is the standard method for pipe wall cross-sections.
Last reviewed August 31, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.